Question

Using Matlab, find an approximation by the method of false position for the root of function f(x) = ex −x2 + 3x−2 accurate to within 10−5 (absolute error) on the interval [0,1]. Please answer and show code.

Pseudo Code for Method of False Position:

Given [a,b] containing a zero of f(x);

tolerance = 1.e-7; nmax = 1000; itcount = 0; error = 1;

while (itcount <=nmax && error >=tolerance)

itcount = itcount + 1;

x= a - ((b-a)/(f(b)-f(a)))f(a)

error =abs(f(x));

If f(a)*f(x) < 0

then b=x;

else a=x;

end while.

Answer 1

clc;
clear all;

format short
f=@(x)exp(x)-x^2 + 3*x-2 ; %function

a=0;b=1; % interval
% checking sign
if(f(b)<f(a))
m=a;
a=b;
b=m;
end

n=1;
err=0.1;
tol=1e-5;

while((err>tol))
  
c=(a*f(b)-b*f(a))/(f(b)-f(a));% false method formula
if ( f(c) == 0 )
break;
elseif ( f(a)*f(c) < 0 )
b = c;
else
a = c;
end
  
err=abs(f(c)); % error
n=n+1; % update next iteration
end
disp('root of function')
c
disp('number of iteration')

%%%%%%%%%%%%%%%%% Answer

root of function

c =

0.2575

number of iteration

n =

5

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